The specific aims of this project are: (1) To determine the relation of medullary concentration gradients and the osmolality of final urine in the mammalian kidney to tubular and vascular permeabilities, flows and architecture. (2) To develop a mathematical model of electrolyte transport in the whole kidney, which includes electrolytes (Na, K, Cl, HC03, H2P04, H), glucose, urea, protein oncotic forces, hydrostatic pressure, and electrical potential. (3) To identify unidirectional membrane permeabilities and regional blood flows from temporal and spatial patterns of radionuclide excretion as determined from CAT scans. The general methodology developed for the solution of non-electrolyte models of the whole kidney will be used to sovle the extended models. Namely, an initial estimate is made of the "global" variables of concentrations, hydrostatic pressure, and electrical potential in the cortical and medullary interstitium. The equations describing flow, concentration, pressure, electric potential, and transmureal fluxes of solutes and water along the tubules and capillaries are then solved, and conservation of mass and electric charge is tested. The estimates of the global variables are then iteratively improved by appropriate mathematical and computational methods until conservation is satisfied to some selected tolerance. This global solution strategy opens the network of interacting feedback loops in whole organ function and allows us to follow any selected variable as a function of any selected model parameter or boundary condition. The long term objective of the research is to develop models that relate normal and pathological renal function to underlying microscopic transport processes in the membranes and cells of the renal tubules and their associated vasculature. More specifically the project focuses on factors affecting the concentration and dilution of urine and sodium excretion in intact and isolated perfused (rat) kidney with the objective of understanding the control of body fluid osmolality and the regulation of extracellular fluid volume. It is relevant to every disease with a disturbance of either.